Alright, let's solve this step-by-step.
1. Understand the problem:
- Grace fills the same number of bags on each of the 5 weekdays.
- Over the weekend, she fills 11 bags.
- In total, she fills 26 bags by the end of the week.
2. Define the variable:
- Let [tex]\( b \)[/tex] represent the number of bags Grace fills each weekday.
3. Set up the equation:
- The total number of bags filled during the 5 weekdays is [tex]\( 5b \)[/tex] (since she fills [tex]\( b \)[/tex] bags each weekday for 5 days).
- Adding the 11 bags filled over the weekend, the equation becomes:
[tex]\[
5b + 11 = 26
\][/tex]
4. Solve the equation:
[tex]\[
5b + 11 = 26
\][/tex]
- Subtract 11 from both sides to isolate the term with the variable [tex]\( b \)[/tex]:
[tex]\[
5b = 26 - 11
\][/tex]
[tex]\[
5b = 15
\][/tex]
- Now, divide both sides by 5 to solve for [tex]\( b \)[/tex]:
[tex]\[
b = \frac{15}{5}
\][/tex]
[tex]\[
b = 3
\][/tex]
So, Grace fills 3 bags of leaves each weekday.
